Consider the setup shown below: a block with mass m1 sits on a table with friction coefficient µ between the table and itself, attached on one side to a spring with stiffness k, and on the other side to a cord with negligible mass that wraps over a frictionless pully and supports a second block with mass m that's suspended in the air over the edge of the table. If the friction between block 1 and the table is not enough to hold up block 2 (so that the spring has to stretch), how far is the spring stretched when the system comes to rest? k m2

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Consider the setup shown below: a block with mass m1 sits on a table with friction coefficient ? between the table and 
itself, attached on one side to a spring with stiffness k, and on the other side to a cord with negligible mass that wraps 
over a frictionless pully and supports a second block with mass m2 that’s suspended in the air over the edge of the table. 
If the friction between block 1 and the table is not enough to hold up block 2 (so that the spring has to stretch), how far 
is the spring stretched when the system comes to rest?
∆? = __________________________________________________________________
?
?1
?2 

*Please write solution and process as much as possible like detail.

**Setup Description:**

A block with mass \( m_1 \) is positioned on a table. The interface between the block and table has a friction coefficient \( \mu \). On one side, the block is connected to a spring with stiffness \( k \). On the opposite side, a cord of negligible mass is attached. This cord passes over a frictionless pulley and is connected to a second block with mass \( m_2 \), which is suspended in the air over the table's edge.

**Problem Statement:**

Given that the friction between block \( m_1 \) and the table is insufficient to support block \( m_2 \) alone (causing the spring to extend), the question is: How much does the spring stretch when the system reaches equilibrium?

**Diagram Explanation:**

- The diagram shows:
  - A horizontal spring labeled \( k \) attached to block \( m_1 \).
  - Block \( m_1 \) is on a horizontal surface with a symbol \( \mu \) indicating friction.
  - A cord leads from block \( m_1 \) over a pulley.
  - Block \( m_2 \) is hanging vertically from the end of the cord beyond the edge of the table.
Transcribed Image Text:**Setup Description:** A block with mass \( m_1 \) is positioned on a table. The interface between the block and table has a friction coefficient \( \mu \). On one side, the block is connected to a spring with stiffness \( k \). On the opposite side, a cord of negligible mass is attached. This cord passes over a frictionless pulley and is connected to a second block with mass \( m_2 \), which is suspended in the air over the table's edge. **Problem Statement:** Given that the friction between block \( m_1 \) and the table is insufficient to support block \( m_2 \) alone (causing the spring to extend), the question is: How much does the spring stretch when the system reaches equilibrium? **Diagram Explanation:** - The diagram shows: - A horizontal spring labeled \( k \) attached to block \( m_1 \). - Block \( m_1 \) is on a horizontal surface with a symbol \( \mu \) indicating friction. - A cord leads from block \( m_1 \) over a pulley. - Block \( m_2 \) is hanging vertically from the end of the cord beyond the edge of the table.
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